The wounds of segregation were still raw in the 1970s. With only rare exceptions, African-American children had nowhere near the same educational opportunities as whites.

The civil rights movement, school desegregation and the War on Poverty helped bring a measure of equity to the playing field. Today, despite some setbacks along the way, racial disparities in education have narrowed significantly. By 2012, the test-score deficit of black 9-, 13- and 17-year-olds in reading and math had been reduced as much as 50 percent compared with what it was 30 to 40 years before.

Achievements like these breathe hope into our belief in the Land of Opportunity. They build trust in education as a leveling force powering economic mobility. “We do have a track record of reducing these inequalities,” said Jane Waldfogel, a professor of social work at Columbia University.

But the question remains: Why did we stop there?

For all the progress in improving educational outcomes among African-American children, the achievement gaps between more affluent and less privileged children is wider than ever, notes Sean Reardon of the Center for Education Policy Analysis at Stanford. Racial disparities are still a stain on American society, but they are no longer the main divider. Today the biggest threat to the American dream is class.

Education is today more critical than ever. College has become virtually a precondition for upward mobility. Men with only a high school diploma earn about a fifth less than they did 35 years ago. The gap between the earnings of students with a college degree and those without one is bigger than ever.

And yet American higher education is increasingly the preserve of the elite. The sons and daughters of college-educated parents are more than twice aslikely to go to college as the children of high school graduates and seven times as likely as those of high school dropouts.

Only 5 percent of Americans ages 25 to 34 whose parents didn’t finish high school have a college degree. By comparison, the average across 20 rich countries in an analysis by the Organization for Economic Cooperation and Development is almost 20 percent.

The problem, of course, doesn’t start in college.

Earlier this week, Professor Waldfogel and colleagues from Australia, Canada and Britain published a new book titled “Too Many Children Left Behind” (Russell Sage). It traces the story of America’s educational disparities across the life cycle of its children, from the day they enter kindergarten to eighth grade.

Their story goes sour very early, and it gets worse as it goes along. On the day they start kindergarten, children from families of low socioeconomic status are already more than a year behind the children of college graduates in their grasp of both reading and math.

And despite the efforts deployed by the American public education system, nine years later the achievement gap, on average, will have widened by somewhere from one-half to two-thirds.

Even the best performers from disadvantaged backgrounds, who enter kindergarten reading as well as the smartest rich kids, fall behind over the course of their schooling.

The challenges such children face compared to their more fortunate peers are enormous. Children from low socioeconomic backgrounds are seven times more likely to have been born to a teenage mother. Only half live with both parents, compared with 83 percent of the children of college graduates.

The children of less educated parents suffer higher obesity rates, have more social and emotional problems and are more likely to report poor or fair health. And because they are much poorer, they are less likely to afford private preschool or the many enrichment opportunities — extra lessons, tutors, music and art, elite sports teams — that richer, better-educated parents lavish on their children.

When they enter the public education system, they are shortchanged again. Eleven-year-olds from the wrong side of the tracks are about one-third more likely to have a novice teacher, according to Professor Waldfogel and her colleagues. They are much more likely to be held back a grade, a surefire way to stunt their development, the researchers say.

Financed mainly by real estate taxes that are more plentiful in neighborhoods with expensive homes, public education is becoming increasingly compartmentalized. Well-funded schools where the children of the affluent can play and learn with each other are cordoned off from the shabbier schools teaching the poor, who are still disproportionally from black or Hispanic backgrounds.

Even efforts to lean against inequality backfire. Research by Rachel Valentino, who received her Ph.D. in education policy at Stanford University this year, found that public prekindergarten programs offered minorities and the poor a lower-quality education.

Perhaps pre-K programs serving poor and minority children have trouble attracting good teachers. Perhaps classrooms with more disadvantaged children are more difficult to manage. Perhaps teachers offer more basic instruction because disadvantaged children need to catch up. In any event, Ms. Valentino told me, “the gaps are huge.”

This is arguably education’s biggest problem. Narrowing proficiency gaps that emerge way before college would probably do more to increase the nation’s college graduation rate than offering universal community college, easier terms on student loans or more financial aid.

“If we could equalize achievement from age zero to 14,” Professor Waldfogel told me, “that would go a long way toward closing the college enrollment and completion gaps.”

It can be done. Australia, Canada — even the historically class-ridden Britain — show much more equitable outcomes.

The policy prescriptions go beyond improving teachers and curriculums, or investing in bringing struggling students up to speed. They include helping parents, too: teaching them best practices in parenting, raising their pay and helping them with the overlapping demands of work and family.

And yet the strains from our world of increasing income inequality raise doubts about our ability to narrow the educational divide. Poorer, less educated parents simply can’t keep up with the rich, who are spending hand over fist to ensure that their children end at the front of the rat race. Our public school system has proved no match to the forces reproducing inequality across the generations.

Fifty years ago, the black-white proficiency gap was one and a half to two times as large as the gap between a child from a family at the top 90th percentile of the income distribution and a child from a family at the 10th percentile, according to Professor Reardon at Stanford. Today, the proficiency gap between the poor and the rich is nearly twice as large as that between black and white children.

In other words, even as one achievement gap narrowed, another opened wide. That kind of progress could dash one’s hope in the leveling power of education.